I love cup-and-cone square taper BBs, but cotters are truly an abomination (in the same category as front indexed shifting, plastic BB cups, stem shifters, and turkey levers). In addition, most cotterless cranksets are riveted together and not very nice. I think replacing the BB with a cartridge unit (discrete spindles and cups are getting harder to find) is a good call unless you're a stickler for keeping everything stock.

No matter what kind of tools you have, removing the fixed cup (the tool you've ordered is for the other cup) will be very difficult on anything this old. Hopefully, it will have happy little wrench flats to grab; if not, Google should tell you how to improvise a clever tool for this purpose.